One of the prettiest vistas I have seen in the Pagosa area is a hike to Piedra Falls. It is quite a drive to get there, but the hike is well worth it.
The hike is not a difficult or long one, nor is elevation a problem. But the view of the fall is spectacular and the flow is sufficient that it is still an impressive sight even on excessively dry years.
There's a little historical museum on the east end of town that's worth a quick look.
To the west a few miles out of town on 160 is Chimney Rock. That's a decent walk and there's Anasazi ruins up at the top (kivas with a view). I'd recommend visiting the kivas off season (fall, winter) when there's nobody around.